US8386099B2 - Method and apparatus for initial orbit determination using high-precision orbit propagation and maneuver modeling - Google Patents
Method and apparatus for initial orbit determination using high-precision orbit propagation and maneuver modeling Download PDFInfo
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- US8386099B2 US8386099B2 US12/656,642 US65664210A US8386099B2 US 8386099 B2 US8386099 B2 US 8386099B2 US 65664210 A US65664210 A US 65664210A US 8386099 B2 US8386099 B2 US 8386099B2
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G3/00—Observing or tracking cosmonautic vehicles
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/242—Orbits and trajectories
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- the present invention relates to orbit determination and maneuver detection. More particularly, the present invention relates to determining orbit state under environments which include full environmental perturbations and satellite maneuvering that requires high fidelity maneuver modeling.
- Orbit determination refers to the estimation of orbits of spacecraft relative to primary celestial bodies, given applicable measurements. Orbit determination methods produce orbit estimates including errors. Orbit determination methods are generally grouped into three categories including Initial Orbit Determination, Batch Least Squares differential corrections, and Sequential Processing.
- IOD Initial Orbit Determination
- An IOD method is generally designed to give an approximation of the orbit of an object, which is then refined with other techniques such as Least Squares, Batch Least Squares and Kalman Filtering.
- Some of the conventional IOD methods developed include Gauss' Method, which uses angle data only; the Herrick-Gibbs method, which uses three position vectors and times; and Lambert's method, which uses two position vectors and time.
- the present invention uses high-precision orbit propagation that includes models of the non-spherical central body, atmospheric drag, solar radiation pressure, and the gravitational attraction of other bodies. Further, high fidelity maneuver modeling and any potential environmental effects on a received signal processed are accounted for orbit determination.
- a method of determining an orbit of an orbital object including: (a) specifying a set of tracking measurement values for the orbit; (b) specifying a force model to represent forces acting on the orbital object; (c) selecting a numerical or analytical integration scheme to compute the object's orbit; (d) specifying known initial conditions including position and velocity for the object; (e) distributing a series of maneuvers over the potential range for which maneuver solutions may occur; (f) applying an orbit propagation scheme to compute the orbit from the initial conditions to the time of the last tracking measurement; (g) computing predicted tracking measurement values based on the orbit computed from the initial conditions; (h) computing a metric based on the differences between the actual and predicted tracking measurements; (i) determining an improved estimate of the initial conditions and/or maneuvers that reduces the metric value of measurement errors using a minimization or root finding algorithm; repeat operations (f) through (i) until the algorithm converges so that the change in the estimated initial conditions is below a predetermined value;
- Another aspect provides a method of determining an orbit of an orbital object including: (a) processing one or more batches of observations of the orbital object; (b) validating the observations; (c) process existing orbit determinations; (d) setting an initial state of the orbit based on (c); (e) setting-up a numerical integrator and force model for the environmental perturbations based on (c); (f) for each observation, adding a propagation segment to integrate the orbit to that point in time; (g) for each propagation, returning the computed measurements value based on the orbit propagation that corresponds with that measurement; (h) setting-up a maneuver in the span where any state correction is expected to have occurred and making the values controllable; (i) setting-up minimization or root finding algorithm to control burn parameters to minimize the error metric to within a predetermined tolerance of all of the computed values, the error being calculated as the difference between the actual measurement at that time and the estimated measurement value at that time based on the orbit propagation; and (j) determining convergence once the root finding algorithm completes solution
- Another aspect provides a system of determining an orbit of an orbital object including: (a) processing one or more batches of observations of the orbital object; (b) validating the observations; (c) process existing orbit determinations; (d) examining measurements to determine the potential maneuver time span; (e) for each measurement in the system, adding a maneuver followed by a propagate segment; (f) setting an initial state based on (c); (g) setting-up a numerical integrator and force model for the environmental perturbations based on (c); (h) for each observation, adding a propagation segment to integrate the orbit to that point in time; (i) for each propagation, returning the computed measurements value based on the orbit propagation that corresponds with that measurement; (j) setting-up a maneuver in the span where any state correction is expected to have occurred and making the values controllable; (k) setting-up a minimization or root finding algorithm to control burn parameters to minimize the error metric to within a predetermined tolerance of all of the computed values, the error metric being calculated as the difference between
- Another aspect provides a method of determining an orbit of an orbital object when an impact event turns the orbital object into one multiple pieces of space debris, the method including: (a) estimating the approximate time of impact on the tracked orbital object; (b) determining the net state change on any piece of debris from the impact as the equivalent of an impulsive maneuver on the piece of debris by; (c) setting-up minimization or root finding algorithm to control the impulsive maneuver and propagate to the measurement time for each piece of debris; (d) setting up a numerical integrator and force model with a nulled-out maneuver for each piece of debris; (e) controlling the maneuver value with the minimization or root finding algorithm to obtain the current observation measurement value; (f) if the solution did converge, archiving the result and post-processing the result with the burn information; (g) if the solution did not converge, flagging the measurement to be re-processed at a later date with modified control values.
- the orbital object may be a satellite.
- FIG. 1 is a flow chart a method of determining an orbit of an orbital object according to a first embodiment of the present invention
- FIG. 2 is a flow chart a method of determining an orbit of an orbital object according to a second embodiment of the present invention
- FIG. 3 is a flow chart a method of determining an orbit of an orbital object according to a third embodiment of the present invention.
- FIG. 4 is a flow chart a method of determining an orbit of an orbital object according to a fourth embodiment of the present invention.
- the present invention uses high-precision orbit propagation, together with a minimization or root finding technique, to determine an initial orbit estimate that best matches a set of tracking measurements. That is, the invention finds the estimated burn conditions that make as small as possible the differences between the actual tracking measurements and the predicted tracking measurements based on the estimated initial conditions. Because tracking measurements contain measurement errors, and the orbit propagation also contains errors, it is generally not possible to find conditions that exactly match the tracking measurements. However, the present invention minimizes the differences in a statistically relevant way that allows the apparatus to determine accurate state and burn information.
- FIG. 1 is a flow chart of a method of determining an orbit of an orbital object according to a first embodiment of the present invention.
- a set of tracking measurement values for the orbit of the orbital object is specified (S 110 ) and a force model to represent forces acting on the orbital object is also specified (S 112 ).
- a numerical or analytical integration scheme to compute the object's orbit is selected (S 114 ).
- known initial conditions including position and velocity for the orbital object are specified (S 116 ).
- a series of maneuvers over the potential range for which maneuver solutions may occur for the orbital object is then determined (S 118 ) and an orbit propagation scheme is applied to compute the orbit from the initial conditions to the time of the last tracking measurement (S 120 ).
- Predicted tracking measurement values based on the orbit computed from the initial conditions are then computed (S 122 ) and the differences between the actual and predicted tracking measurements are also computed (S 124 ).
- the orbital object may be a satellite.
- FIG. 2 is a flow chart a method of determining an orbit of an orbital object according to a first embodiment of the present invention directed to a standard orbit and burn profile, where maneuver durations are such that they occur before the measurements to process.
- one or more batches of observations come into the system for processing (S 210 ) and new measurements are validated to be “reasonable” given the extremes in the variations of the orbit physics among the various measurements (S 215 ). For example, if two measurements a few seconds apart show a variation far in excess allowable by the speed of light then that would be indicative of a problem.
- Further operations include setting up an initial state of the orbit based on Operation S 220 (S 235 ), setting-up a numerical integrator and force model for the environmental perturbations based on Operation S 220 (S 240 ), for each observation, adding a propagation segment to integrate the orbit to that point in time (S 245 ), for each propagation, returning the computed measurements value based on the orbit propagation that corresponds with that measurement (S 250 ), setting-up a maneuver in the span where any state correction is expected to have occurred and making the values controllable (S 255 ), setting-up a minimization algorithm to control burn parameters to minimize the error to within a predetermined tolerance of all of the computed values, the error being calculated as the difference between the actual measurement at that time and the estimated measurement value at that time based on the orbit propagation (S 260 ).
- convergence is determined once the minimization or root finding algorithm completes solution (S 265 ).
- the system can be re-run with different parameters to try and achieve convergence. This could be things like varying the inputs to the root finding algorithm such as the step size used in testing the control parameters, changing the control parameters based on various appropriate constrained burn settings, et cetera.
- FIG. 3 present an embodiment of the present invention of a method for determination of an orbit of an orbital object where the maneuvers of the orbital object are long enough to be interspersed with the measurements, such as multi-hour ion engine burns, which more effectively takes into account system dynamics.
- one or more batches of observations come into the system for processing (S 310 ) and new measurements are validated to be “reasonable” given the extremes in the variations of the orbit physics among the various measurements (S 315 ). For example, if two measurements a few seconds apart show a variation far in excess allowable by the speed of light then that would be indicative of a problem.
- Further operations include setting-up an initial state of the orbit based on Operation S 320 (S 335 ), setting-up a numerical integrator and force model for the environmental perturbations based on Operation S 320 (S 340 ), for each observation, adding a propagation segment to integrate the orbit to that point in time (S 345 ), for each propagation, returning the computed measurements value based on the orbit propagation that corresponds with that measurement (S 350 ), setting-up a maneuver in the span where any state correction is expected to have occurred and making the values controllable (S 355 ), setting-up a weighted least squares algorithm to control burn parameters to minimize the error to within a predetermined tolerance of all of the computed values, the error being calculated as the difference between the actual measurement at that time and the estimated measurement value at that time based on the orbit propagation (S 360 ).
- convergence is determined once the root finding algorithm completes solution (S 365 ).
- the method can be repeated with different parameters to try and achieve convergence. This could be affected by varying the inputs to the root finding algorithm such as the step size used in testing the control parameters, changing the control parameters based on various appropriate constrained burn settings, et cetera.
- the overall span of the maneuver is determined as well as the integrated burn information. This is done by examining each of the maneuvers. A maneuver, versus relatively small errors, inherent in force modeling, will show up as an estimated maneuver of a sufficiently large value, by comparison. By examining the time span of maneuvers where the maneuvers are large the maneuver start and stop times can be estimated.
- the maneuver stop time is searched for, to determine if the burn was still on-going at the last measurement. If no burn stop was found then it can assumed that the maneuver is still ongoing. This information, along with the up-to-date burn information can be passed back out of the system.
- burn stop If a burn stop was found then there is a total burn solution.
- burns are integrated to determine the net burn data, including start time, stop time, direction, magnitude, et cetera. Once the maneuver is numerically integrated the system then checks the results to make sure that the integrated results still maintain convergence of the system.
- the present invention is able to take the observation measurements and the pre-collision assessment to correlate each individual measurement to each piece of debris in a manner that allows for early orbit determinations for each of the new pieces of space debris.
- the net state change on any piece of debris from the impact will be the equivalent of an impulsive maneuver on said piece.
- the impact is treated as an impulsive maneuver to simulate the state change.
- a root finder is setup to control the impulsive maneuver and propagate to the measurement time.
- the expected measurement value is returned at the end of the propagation segment and is used as the constraint on the root finder.
- the numerical integrator and force model is setup with a nulled-out maneuver and the root finder method controls the maneuver value to be able to reach the current observation measurement value.
- the root finder is run to look for a solution. If the solution did converge then this result will be archived, with the burn information and other values for post processing.
- the measurement is flagged to be re-processed at a later date with modified control values. If there is more data to process then reset the system, push the new data point restart the process. If there are no more measurements then the data is ready for post processing to determine the number of correlated elements in the debris cloud and the post-impact state of said objects. For each maneuver look to see if they correspond to a prior-maneuver estimate. If they do correlate then these are multiple measurements of the same object. If they do not then this corresponds to a new piece of debris. Aggregate all solutions that correlate for each debris component to distill out the debris cloud data.
- the aggregated measurement data is processed for each piece of debris separately to refine the solution for debris with multiple measurements.
- a list of post-impact debris components is generated with their corresponding state values and the catalog is then exported to other flight dynamics or navigation software.
- FIG. 4 shows a flow chart of a method of determining an orbit of an orbital object when an impact event turns the orbital object into one multiple pieces of space debris.
- the method of determining an orbit of an orbital object when an impact event turns the orbital object into one multiple pieces of space debris begins with estimating the approximate time of impact on the tracked orbital object (S 410 ).
- the net state change on any piece of debris from the impact as the equivalent of an impulsive maneuver on the piece of debris is determined (S 420 ).
- a root finder is set up to control the impulsive maneuver and propagate to the measurement time for each piece of debris (S 430 ).
- a numerical integrator and force model with a nulled-out maneuver for each piece of debris is then set up (S 440 ). Subsequently, the maneuver value is controlled with the root finder to obtain the current observation measurement value (S 450 ). If the solution converges, the result is archived and post-processed with the burn information (S 460 ). If the solution does not converge, the measurement is flagged to be re-processed at a later date with modified control values (S 470 ).
- the above-described embodiments of the present invention can be realized as apparatuses including a computer, where the computer includes a computer readable medium containing processing instructions for implementing the above described methods.
- the computer readable medium may be a storage media, such as a magnetic storage medium (for example, a ROM, a floppy disc, or a hard disc) or an optical readable medium.
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US20150149001A1 (en) * | 2013-11-27 | 2015-05-28 | Analytical Graphics Inc. | Maneuver processing |
US9540122B2 (en) * | 2013-11-27 | 2017-01-10 | Analytical Graphics Inc. | Maneuver processing |
US9617018B2 (en) | 2014-03-28 | 2017-04-11 | Rincon Research Corporation | Automated detection and characterization of earth-orbiting satellite maneuvers |
US20170139427A1 (en) * | 2015-01-07 | 2017-05-18 | Mitsubishi Electric Research Laboratories, Inc. | Model Predictive Control of Spacecraft |
US9874879B2 (en) * | 2015-01-07 | 2018-01-23 | Mitsubishi Electric Research Laboratories, Inc. | Model Predictive control of spacecraft |
US20220041308A1 (en) * | 2019-06-04 | 2022-02-10 | Ihi Corporation | Method for estimating right-under point position of on-orbit object |
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